AL-LAFITAAT, Egypt, March 16 (Reuters) - Egypt's army says it is crushing Islamist militants in the Sinai Peninsula, but in the region's villages and towns a victory for the state feels a long way off.

In a rare visit to eight villages in Northern Sinai last week, a Reuters reporter saw widespread destruction caused by army operations, but also found evidence that a few hundred militants are successfully playing a cat-and-mouse game with the Arab world's biggest army and are nowhere near defeat. It is increasingly difficult for foreign correspondents to openly enter conflict zones in the Sinai.

Residents say the militants - a mix of Egyptian Islamists, foreign fighters and disgruntled youth - have seized control of about a third of the villages in the region and are now taking their fight closer to Cairo.

"The army is in control of the main roads but is unable to enter many villages. It can only attack them by helicopter," said Mustafa Abu Salman, who lives near al-Bars village.

"Even when the army's armoured personnel vehicles enter villages they fail to arrest militants who have better knowledge of the place, which the military completely lacks."

Many residents say that the authorities' military operations are actually creating new enemies for the state.

The fight against militant Islam is a key test for the interim government in Cairo. Sinai-based militants stepped up attacks on police and soldiers last year, soon after Egypt's army toppled Islamist President Mohamed Mursi and tried him on a wide range of charges. The violence has left 300 people dead and hammered Egypt's economy, which has not recovered from the political turmoil that began in early 2011 when a popular uprising ousted Hosni Mubarak.

The army and the government say they are beating the militants. In an attempt to stop the illegal flow of arms, Egyptian authorities have destroyed thousands of tunnels that ran under the border between Egypt and the Gaza Strip, which borders North Sinai. Almost every night, Apache helicopters fire rockets at suspected Islamist militant hideouts in the houses and farms of the largely lawless peninsula, a 61,000 sq km (24,000 sq mile) area wedged between the Suez Canal to the west and Israel and Gaza to the east.

"We are doing an extremely good job but that does not mean we have completely ended terrorism," army spokesman Ahmed Ali told Reuters. "It is a vicious war because the terrorists have light and heavy weapons. The lives of the people in Sinai are of great importance for the armed forces and they are seen as the foundation for national security in that area."

Army chief Field Marshal Abdel Fattah al-Sisi, who is expected to become Egypt's next president, owes much of his popularity to his ouster of Mursi's Muslim Brotherhood and his tough stance against the militants.

Sisi has described the Sinai operation as an ongoing security campaign to rid the region of extremists and criminals. The Sinai, he has said, is a top security priority.

So far, though, local residents say the military is making little progress. The army's blunt tactic of rocketing suspected hideouts is failing, they say, because the militants have mastered the terrain. They move around villages using alleyways where it is difficult to spot them from the air, and mix with civilians or hide in olive groves. The effort to stop the flow of weapons is also a struggle, they say, in large part because smugglers are bringing in weapons from Libya. Residents say the number of fighters has decreased in the past few months, partly because many fighters have moved towards the Nile Valley.

"The army has entered a war, but it is not specialised in this type of war, which requires special counter-insurgency forces, not an army," said Mussab Abu Fajr, a Bedouin leader in the Sinai's main city of al-Arish.

Major-General Samih Bishady, the head of security in North Sinai, said that the army has "killed and arrested many of the wanted in Sinai." He put the number of active militants remaining there at just 80. At the same time, he and other officials in Cairo agree that many Islamist fighters have moved to the Nile Delta, bringing the conflict much closer to the capital and Egypt's main population centres.

CHANGE OF TACTICS

Standing beside two olive trees outside the village of al-Lafitaat, a senior militant who would be identified only by his initials, S.A., set out the way the groups' tactics have changed.

"At the start of the fighting we used to hide in mountains but now we are present in the villages among residents, because it is safer there," he said. "When we were in the mountains it was easy for the army to strike us with helicopters. But as long as we are with the people it is hard to reach us."

S.A. said that he and his fellow fighters use simple home-made bombs such as jam jars stuffed with dynamite. The devices are hidden in olive trees or on the side of road, with desert sand covering detonation cords. He said the militants wait on hilltops for military convoys to pass and then detonate their bombs by remote control, using cellphone identification cards.

"We use cooking cylinders and water jugs and we will pack them with explosives, and connect them to timers and a SIM card and we plant them on roads we know are used by the army," said S.A.

The threat of roadside bombs has prompted the army to cut mobile phone networks and the Internet during daylight hours when military vehicles move around.

"The militants are dealing with us in haphazard primitive ways and they have entered a dirty war with us," said a military official in Sinai who declined to be identified.

In an effort to evade the attention of the military, many residents now hang several Egyptian flags on their homes as a gesture of loyalty to the state.

Ahmed Abu Gerida, who lives in al-Bars village, said militants sometimes hide in civilians' houses to avoid detection. "They hang up women's clothes, including bras and underwear, because they know the army will hesitate to approach Bedouin women," he said. "One time soldiers entered one of these homes and found a storage place for explosives and blew up the house."

Air strikes, launched almost daily since Mursi's fall, have hammered villages like al-Lafitaat, where all 12 single-storey cement houses have been destroyed or heavily damaged over the past few months. Some were reduced to a few beams, while others were burnt out, their ceilings collapsed. Residents fled, leaving behind a handful of sheep.

One woman named Ni'imaa stood next to the remnants of her house with her two children, after returning a few days earlier to retrieve her belongings. She collected a pillow, a mattress, some dishes and a small stove and placed them in a pick-up truck. She said the army killed her husband, who she said was not a militant, four months ago.

"We want to go to a safe spot with my children. As you can see a rocket destroyed half of my house and I will not wait until the other half gets destroyed."

Army spokesman Ali said: "We try by all ways to avoid having innocent civilian casualties during these clashes with the terrorists. The terrorists use these tactics of targeting civilians so that they can make the armed forces lose the support of the people in Sinai. There are some losses in the clashes that are caused by extremists."

"BETWEEN TWO FIRES"

Residents have become familiar with the rituals of the conflict. Every day at 4pm the army closes the main streets in every village. At night, a buzzing noise overhead is a sign that rockets may follow. Sinai residents and some Egyptian security officials believe the noise is made by drones, perhaps from Israel; Islamist militant groups in the Sinai are seen as a security threat to the Jewish state.

The Egyptian military says it does not target civilians. A military officer at a checkpoint in al-Masoura village said the army only attacks villages which are occupied by militants.

"Some innocents die but at the hands of terrorists not us."

But residents say the military campaign is fanning resentment in a population that already felt neglected by the central government. The Bedouin population has long accused the Egyptian authorities of neglecting the Sinai region, failing to provide basic services and jobs.

"The military operations hit the wanted and unwanted," said Mona Barhouma, who lives in Rafah and complains that innocent people are regularly killed.

Even residents who are opposed to militants say they are scared to cooperate with the army, which has appealed for tips to find the fighters.

Sheikh Hassan Khalaf, who heads the Sawarka tribe in Sinai, said 35 Sinai residents who gave the army information on militants had been shot dead in the past three months. The army confirmed the shooting, but not the numbers involved.

Many people feel trapped between both sides.

"We are between two fires. If we report the terrorists to the army, the militants will kill us the next day," said Subayha, a Bedouin who said that she and her children struggle to sleep because of army shelling in her village of al-Mahdiya. For safety, they sometimes sleep outside the gates of a building that houses international peacekeepers, she says.

"If we remain silent the army considers us allies of the terrorists and can start attacking our villages," said Subayha.

Cuts to the mobile phone network and Internet have added to public frustration.

SISI'S BIG CHALLENGE

Aside from responding to calls for holy war, militants are given worldly incentives, according to residents and security officials. They say leaders offer young recruits wives, money and homes in return for a commitment to carry out suicide bombings. "They have the good life for a few months and are promised it will only get better in paradise after the operation," said Bishady, the head of security in North Sinai.

Egyptian security officials say combatants include Egyptian fighters as well as some from Hamas, the Palestinian group that controls the Gaza Strip, and from Afghanistan. They believe some of the Egyptian fighters spent time in Taliban-controlled areas in Pakistan, returning after the election of Mursi in 2012.

The army-backed government accused Mursi of allowing militancy to flourish in the Sinai by freeing hardcore Islamists from jail. Security chief Bishady said that during Mursi's rule he saw presidential vehicles transport officials to meetings with Islamists. Army officials also say those talks took place.

Khalaf, the Sawarka tribal leader, said he saw Mohamed al-Zawahri, the brother of al Qaeda chief Ayman al-Zawihri, in a presidential car. Sinai police were not allowed to approach the convoys or meetings, said Khalaf.

Senior Muslim Brotherhood official Mohamed Saleh told Reuters: "There is no evidence of this. It is all lies spread in an attempt to hurt the reputation of the Muslim Brotherhood. We have never associated in our history with any groups that hurt Egypt."

Wael Haddara, a senior adviser to Mursi while he was president, said Mursi's public "efforts to reach out to bona fide tribal elders and leaders" might now be "cast as a meeting with terrorists". The Brotherhood has said it released prisoners when it was in power because the prisoners had been unfairly tried or had served their sentences.

At the same time, senior Brotherhood leader Mohamed el-Beltagy said last year after Mursi's fall that the violence in the Sinai would stop if the army reversed what the Muslim Brotherhood calls a coup.

The big fear is that the conflict is spreading. Ansar Bayt al-Maqdis, the best-known Sinai-based militant group, has claimed responsibility for several high-profile attacks in Cairo in recent months, including a suicide bombing that failed to kill the interior minister last September. The group also said it shot down a military helicopter in January, killing five soldiers.

An army official in Cairo said the Sinai militants had made a strategic move to shift operations to other places in Egypt. If Sisi becomes president, the attacks are most probably going to increase, as in militants' eyes, Egypt will be "officially run by a military regime," he said.

"This will be the biggest challenge to Sisi's rule." (The name of the correspondent is being withheld for security reasons; Additional reporting by Asma Alsharif; Editing by Yasmine Saleh and Michael Georgy)